Polygon KLMN is similar to polygon PQRS. What is the length of QR? *
K.3m L
P 4.5m Q
4m
4m
N.3m. M
16m
R
S 4.5m
9m
8m
6m
It is not possible to determine the length of QR without additional information.
To determine the length of QR, we need to compare the corresponding sides of the similar polygons KLMN and PQRS. According to the given information, the corresponding sides KL and PQ have lengths of 3m and 4.5m, respectively.
We can set up a proportion to find the length of QR:
KL / PQ = QR / RS
Substituting the given values:
3m / 4.5m = QR / RS
Solving for QR:
QR = (3m / 4.5m) * RS
Looking at the given options, we see that RS has a length of 4.5m.
QR = (3m / 4.5m) * 4.5m
QR = 3m
Therefore, the length of QR is 3m.
To determine the length of QR, we need to use the concept of similarity between the polygons KLMN and PQRS. When two polygons are similar, it means that their corresponding angles are equal, and their corresponding sides are proportional.
Since we know the lengths of KL, LM, and MN, we can use this information to find the scale factor between the two polygons.
First, we calculate the scale factor between the lengths of the corresponding sides. The length of KL is 3m, and the length of PQ is 4.5m. The scale factor can be determined by dividing the length of PQ by KL:
Scale factor = Length of PQ / Length of KL = 4.5m / 3m = 1.5
This means that the corresponding sides are scaled up by a factor of 1.5 from polygon KLMN to PQRS.
Next, we apply the scale factor to find the length of QR. We already know that the length of MN is 3m. To find QR, we need to multiply the length of MN by the scale factor:
Length of QR = Length of MN * Scale factor = 3m * 1.5 = 4.5m
Therefore, the length of QR is 4.5m.